Sturm-Liouville Equation. Question about different forms.

1. Nov 25, 2014

DiogenesTorch

I have noticed the following 2 different forms for the Sturm-Liouville equation online, in different texts, and in lectures.

$[p(x) y']'+q(x)y+\lambda r(x) y = 0$

$-[p(x) y']'+q(x)y+\lambda r(x) y = 0$

Does it make a difference? I am guessing not as the negative can just be absorbed into function $p(x)$?

But I am still scratching my head as to why some texts use the negative sign in front of the 1st term. Is there some advantage to doing so?

2. Nov 25, 2014

ShayanJ

I don't think there is much difference. In fact, I think the difference is the same as the difference between people who like to eat a special food with different sauces!!!

3. Nov 25, 2014

DiogenesTorch

lol the extra special sauce.

Seriously though I just wondered if somewhere the use of the negative sign has some sort of a practical reason. Like for example when solving partial differential equations using the separation of variables method, we sometimes for convenience stick a minus sign in front of eigenvalue/"separation constant."

4. Nov 25, 2014

ShayanJ

I sometimes do things with Sturm-Liouville theory and I don't put that minus sign there and never encountered a problem which can be solved by that minus sign!

5. Nov 25, 2014

DiogenesTorch

Cool just wondered if it ever mattered. Thanks Shyan much appreciated :)